Finite Group Databasebeta

← C43×#9530 #24929547

Subgroups — C43×#9530 #24929547

Order 11008.

428 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3110C211yesmaximal, characteristic
2C43×#2985C211yesmaximal, characteristic, complemented
3C43×#1559C211yesmaximal, characteristic, complemented
4C43×#1486C211yesmaximal, characteristic
5C43×#1466C211yesmaximal, characteristic
6C43×#1307C211yesmaximal, characteristic, complemented
7C43×#1287C211yesmaximal, characteristic, complemented
8C43×#533C2211yescharacteristic
9C2×C4×D4×C43C2211yescharacteristic
10C43×#484C412yes—
11C43×#474—21no—
12C43×#461—21no—
13C43×#450C412yes—
14C43×#446—22no—
15C43×#446—21no—
16C8×Q8×C43—21no—
17C43×#440—22no—
18C43×#433—22no—
19C43×#432C2211yescharacteristic
20C43×#432C2211yescharacteristic
21C43×#432C2211yescharacteristic
22C43×#431C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C43×#333—21no—
25C43×#332—21no—
26C43×D4⋊C8—21no—
27C43×D4⋊C8—21no—
28C43×#323—22no—
29C22×D4×C43C2×C411yescharacteristic
30C23×C4×C43—21no—
31C2×SD16×C43—22no—
32C2×M16×C43—21no—
33C4⋊Q8×C43D411yescharacteristic
34C4⋊Q8×C43D411yescharacteristic
35#125×C43—21no—
36C22⋊Q8×C43—21no—
37C22⋊Q8×C43C2×C412yes—
38C4×Q8×C43—21no—
39C4×Q8×C43D412yes—
40C4×D4×C43—21no—
41C4×D4×C43—21no—
42C4×D4×C43—21no—
43C4×D4×C43—21no—
44#117×C43—21no—
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C42×C43C2311yescharacteristic
48#107×C43—22no—
49C4⋊C8×C43—22no—
50C4⋊C8×C43—22no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43—21no—
57#103×C43—22no—
58#102×C43—22no—
59C22⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43C2×C412yes—
62C22⋊C8×C43D412yes—
63#97×C43—22no—
64#97×C43—21no—
65#97×C43—21no—
66#97×C43—21no—
67C4×C8×C43—22no—
68C4×C8×C43D411yescharacteristic
69C4×C8×C43D411yescharacteristic
70C24×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43C22⋊C412yes—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—42no—
76C22×C4×C43—21no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43—81no—
80C22×C4×C43—81no—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84SD16×C43—44no—
85M16×C43—81no—
86C2×C8×C43—22no—
87C2×C8×C43—21no—
88C2×C8×C43—22no—
89C2×C8×C43—21no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43C22⋊C412yes—
100C22⋊C4×C43—22no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—22no—
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108C23×C43—22no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—81no—
112C23×C43—81no—
113C23×C43C4×D411yescharacteristic
114Q8×C43—42no—
115Q8×C43—41no—
116Q8×C43—41no—
117D4×C43—22no—
118D4×C43—22no—
119D4×C43—41no—
120D4×C43—41no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—82no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C8×C43—41no—
139C8×C43—42no—
140C8×C43—41no—
141C8×C43—42no—
142C8×C43—81no—
143C8×C43—81no—
144#9530C4311yesmaximal, characteristic, direct product factor, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—42no—
149C22×C43—82no—
150C22×C43—82no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43#38611yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—42no—
161C4×C43—81no—
162C4×C43#47111yescharacteristic
163C4×C43#47211yescharacteristic
164#3110C2×C4311yescharacteristic
165#2985C2×C4311yescharacteristic, complemented
166#1559C2×C4311yescharacteristic, complemented
167#1486C2×C4311yescharacteristic
168#1466C2×C4311yescharacteristic
169#1307C2×C4311yescharacteristic, complemented
170#1287C2×C4311yescharacteristic, complemented
171C2×C43—41no—
172C2×C43—82no—
173C2×C43#189111yescharacteristic
174C2×C43#190511yescharacteristic
175C2×C43#190711yescharacteristic
176#533C22×C4311yescharacteristic
177C2×C4×D4C22×C4311yescharacteristic
178#484C4×C4312yes—
179#474—21no—
180#461—21no—
181#450C4×C4312yes—
182#446—22no—
183#446—21no—
184C8×Q8—21no—
185#440—22no—
186#433—22no—
187#432C22×C4311yescharacteristic
188#432C22×C4311yescharacteristic
189#432C22×C4311yescharacteristic
190#431C22×C4311yescharacteristic
191#423C22×C4311yescharacteristic
192#333—21no—
193#332—21no—
194D4⋊C8—21no—
195D4⋊C8—21no—
196#323—22no—
197C43#953011yescharacteristic, direct product factor, Sylow
198C22×D4C2×C4×C4311yescharacteristic
199C23×C4—21no—
200C2×SD16—22no—
201C2×M16—21no—
202C4⋊Q8D4×C4311yescharacteristic
203C4⋊Q8D4×C4311yescharacteristic
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8C2×C4×C4312yes—
207C4×Q8—21no—
208C4×Q8D4×C4312yes—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213#117—21no—
214C2×C4⋊C4C2×C4×C4311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C42C23×C4311yescharacteristic
217#107—22no—
218C4⋊C8—22no—
219C4⋊C8—22no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226#103—22no—
227#102—22no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8C2×C4×C4312yes—
231C22⋊C8D4×C4312yes—
232#97—22no—
233#97—21no—
234#97—21no—
235#97—21no—
236C4×C8—22no—
237C4×C8D4×C4311yescharacteristic
238C4×C8D4×C4311yescharacteristic
239C24—21no—
240C2×Q8—21no—
241C2×Q8C22⋊C4×C4312yes—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—42no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4C22×C4×C4311yescharacteristic
251C22×C4C2×D4×C4311yescharacteristic
252C22×C4#41×C4311yescharacteristic
253SD16—44no—
254M16—81no—
255C2×C8—22no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4C22⋊C4×C4312yes—
269C22⋊C4—22no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C42—22no—
273C42C2×D4×C4311yescharacteristic
274C42C2×D4×C4311yescharacteristic
275C42C2×D4×C4311yescharacteristic
276C42#41×C4311yescharacteristic
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23C4×D4×C4311yescharacteristic
283Q8—42no—
284Q8—41no—
285Q8—41no—
286D4—22no—
287D4—22no—
288D4—41no—
289D4—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×C22⋊C4×C4311yescharacteristic
302C2×C4C4×D4×C4311yescharacteristic
303C2×C4#120×C4311yescharacteristic
304C2×C4#121×C4311yescharacteristic
305C2×C4#121×C4311yescharacteristic
306C2×C4#123×C4311yescharacteristic
307C8—42no—
308C8—41no—
309C8—42no—
310C8—41no—
311C8—81no—
312C8—81no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—82no—
318C22—82no—
319C22—81no—
320C22—81no—
321C22C43×#38611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—81no—
330C4C43×#47111yescharacteristic
331C4C43×#47211yescharacteristic
332C2—41no—
333C2—82no—
334C2C43×#189111yescharacteristic
335C2C43×#190511yescharacteristic
336C2C43×#190711yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C43×#2985C2semidirect
3. C43×#1559C2semidirect
6. C43×#1307C2semidirect
7. C43×#1287C2semidirect
144. #9530C43direct (N × H)
165. #2985C2×C43semidirect
166. #1559C2×C43semidirect
169. #1307C2×C43semidirect
170. #1287C2×C43semidirect
197. C43#9530direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#31102
C43×#29852
C43×#15592
C43×#14862
C43×#14662
C43×#13072
C43×#12872
#953043